1
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Let z and $$\omega$$ be two complex numbers such that $$\omega = z\overline z - 2z + 2,\left| {{{z + i} \over {z - 3i}}} \right| = 1$$ and Re($$\omega$$) has minimum value. Then, the minimum value of n $$\in$$ N for which $$\omega$$n is real, is equal to ______________.
2
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Let z be those complex numbers which satisfy

| z + 5 | $$\le$$ 4 and z(1 + i) + $$\overline z$$(1 $$-$$ i) $$\ge$$ $$-$$10, i = $$\sqrt { - 1}$$.

If the maximum value of | z + 1 |2 is $$\alpha$$ + $$\beta$$$$\sqrt 2$$, then the value of ($$\alpha$$ + $$\beta$$) is ____________.
3
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
Let $$i = \sqrt { - 1}$$. If $${{{{\left( { - 1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 - i)}^{24}}}} + {{{{\left( {1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 + i)}^{24}}}} = k$$, and $$n = [|k|]$$ be the greatest integral part of | k |. Then $$\sum\limits_{j = 0}^{n + 5} {{{(j + 5)}^2} - \sum\limits_{j = 0}^{n + 5} {(j + 5)} }$$ is equal to _________.
4
JEE Main 2021 (Online) 24th February Morning Shift
Numerical
+4
-1
If the least and the largest real values of a, for which the
equation z + $$\alpha$$|z – 1| + 2i = 0 (z $$\in$$ C and i = $$\sqrt { - 1}$$) has a solution, are p and q respectively; then 4(p2 + q2) is equal to __________.